Nonexistence of bounded solutions of one dimensional wave equations with quasiperiodic forcing terms (Q1914823)

The author constructs a class of quasiperiodic forcing terms for which every solution \(u(x,t)\) of the initial, boundary-value problem for the one-dimensional wave equation is unbounded in \(t\in\mathbb{R}^1\). To this end, the author first obtains the basic frequencies as the solutions of an algebraic equation so as to satisfy Diophantine approximation inequalities. This result is used to construct a class of quasiperiodic functions to which the forcing term belongs.